Locally definite operators in indefinite inner product spaces (Q1364560)

Let \(A\) be a selfadjoint operator in a Krein space. It is shown that if an interval \(\Delta\) of the real axis consists only of spectral points of positive (or negative) type of \(A\) then \(A\) has a spectral function on \(\Delta\). Another main result states that under a compact selfadjoint perturbation a point of such an interval \(\Delta\) either remains a point of positive (negative, respectively) type or becomes an eigenvalue of finite index of negativity (positivity, respectively). Some of these results remain true for a larger class of indefinite inner product spaces.